1. Field of the Invention
The present invention relates to a method of alignment, and more particularly relates to a method of alignment for an exposure step in a manufacturing process of a semiconductor device.
2. Description of the Background Art
An exposure apparatus has been known in which a circuit pattern on a photomask or reticle is superimposed on and transferred onto a circuit pattern formed on a semiconductor wafer in a process of manufacturing a semiconductor device. The exposure apparatus is usually referred to as a stepper. The stepper demagnificates a pattern layer formed on the reticle using a projection lens and successively exposes it onto each shot region on one piece of wafer, moving the wafer step by step under the projection lens. FIG. 2 is a flow chart schematically showing an exposure sequence according to the conventional enhanced global alignment (EGA) method. The flow chart is disclosed in Japanese Patent Laying-Open No. 61-44429.
With reference to FIG. 2, according to the alignment method, prealignment of a wafer is first performed using an orientation flat of the wafer (step D10). The entire wafer is thereafter corrected by rotation utilizing wafer global alignment (WGA) marks formed in each shot region (step D11). The WGA mark is an alignment mark for the alignment of the entire wafer.
A wafer stage is then displaced based on a design value of a chip array. In a plurality of shot regions set for detecting an error, positions of laser step alignment (LSA) marks of a pattern printed on the region are detected by an LSA optical system. The LSA alignment mark is for the alignment of the shot in the wafer provided in order to allow finer alignment compared to above mentioned WGA mark.
Position of the wafer stage is detected by a laser interference system simultaneously with the detection of the position of the LSA alignment mark. Based on a detected value, a registration error between the printed pattern on the wafer and the reticle pattern is detected (step D12).
A deviation is determined from the registration error in each shot region and a position coordinate of the wafer stage (coordinate of the printed pattern). An average value of the deviation is determined as a correction value (error parameter) (step D13).
A chip array map in which the error is corrected is formed from the error parameter and the design value (step D14). Six of the error parameters, X offset, Y offset, X scaling, Y scaling, X rotation, and Y rotation, are used. The X offset and the Y offset are respectively amounts of shift in an X axis direction and a Y axis direction in orthogonal XY axes. The X scaling and the Y scaling are amounts of shift due to expansion and contraction in the X axis direction and the Y axis direction, respectively. The X rotation and the Y rotation are amounts of shift due to rotation of the X axis and the Y axis, respectively. The position of the wafer stage is determined by the step and repeat approach according to the chip array map formed from the error parameters and the design value (step D15). Each shot region is thereafter exposed (step D16).
The alignment has conventionally been conducted using the six error parameters as described above. In order to make the conventional method more precise, a method of correction using additional error parameters is proposed.
According to the proposed method, a shot rotation error and a shot magnifying rate error, that are error parameters in the shot region, are further utilized in addition to the above described six error parameters. FIG. 3 is a schematic diagram showing a positioning procedure (alignment sequence) according to the proposed method. With reference to FIG. 3, according to this method, alignment in a step B is performed based on step A, and alignment in a step C is performed based on the step B. Alignment in a step D is carried out based on an alignment mark in the X axis direction in the step B, as well as an alignment mark in the Y axis direction in the step C. At the time of alignment for respective steps B, C, and D, the alignment is achieved by determining a correction value using the six error parameters (array error) and the rotation and magnifying rate errors of the shot (shot errors).
A problem in the method of alignment shown in FIG. 3 is difficulty in making the correction of the shot error properly. More specifically, although the array error can be corrected independently in the X and Y axes directions, independent correction of the shot rotation error and the magnifying rate error is impossible since the errors in the X and Y axes directions are related to each other. A problem when the alignment marks in the X axis direction and the Y axis direction are superimposed on corresponding marks in separate steps as the case of the step D, is that shift of the position is increased if correction is made using the shot rotation error and magnifying rate error. This is further described with reference to FIGS. 4-19.
FIGS. 4-19 show the rotation error only. Referring to FIG. 4, a representative rotation error in a shot is described. The shot rotation error is constituted by the sum of a constant error (b) and a dispersive error (.DELTA.b). In this case, the constant error (b) is considered a fixed value, so that the range of the shot rotation error is b.+-..DELTA.b.
FIG. 5 is a systematic diagram showing a pattern in which a shot rotation error is generated in the steps B, C and D steps shown in FIG. 3. With reference to FIG. 5, the maximum error at the time of alignment performed in the step C with respect to the step B is b+.DELTA.b (in the case of 2), and the minimum error is b-.DELTA.b (in the case of 1). When the alignment in the step D is performed for the maximum error 2 and the minimum error 1 respectively, further maximum errors (1-2, 2-2) as well as further minimum errors (1-1, 2-1) are generated respectively for the cases of 1 and 2. FIG. 6 shows the case of 1 in FIG. 5, FIGS. 7-9 show the case of 1-1 in FIG. 5, FIGS. 10-12 show the case of 1-2 in FIG. 5, FIG. 13 shows the case of 2 in FIG. 5, FIGS. 14-16 show the case of 2-1 in FIG. 5, and FIGS. 17-19 show the case of 2-2 in FIG. 5. When the alignment in the step D is performed, the step D is usually performed between the steps B and C.
With reference to FIG. 6, in the case of 1 shown in FIG. 5, the error in the step C with respect to the step B is b-.DELTA.b. The alignment in the step D is desirably performed between the steps B and C. In this case, if the rotation error in the step D with respect to the step C is .alpha., and the rotation error in the step D with respect to the step B is .beta., .alpha. and .beta. are expressed by following expressions (1) and (2). Here, b&gt;0, b&gt;.DELTA.b, and the clockwise direction from D is assumed to be positive. EQU .alpha.=(-1)(b-.DELTA.b)/2 (1) EQU .beta.=(b-.DELTA.b)/2 (2)
With reference to FIGS. 7-9 next, .vertline..alpha..vertline., .vertline..beta..vertline., .vertline..gamma..vertline., .vertline..omega..sub.c .vertline., .omega..sub.c, .vertline..omega..sub.b .vertline., and .omega..sub.b are respectively expressed by the following expressions (3)-(9). EQU .vertline..alpha..vertline.=(b-.DELTA.b)/2 (3) EQU .vertline..beta..vertline.=(b-.DELTA.b)/2 (4) EQU .vertline..gamma..vertline.=b-.DELTA.b (5) ##EQU1## Since D is in a counterclockwise direction with respect to C as shown in FIG. 7, following expressions are derived. EQU .omega..sub.c =-(b-.DELTA.b)/2 (7) ##EQU2## EQU .omega..sub.b =-(b-.DELTA.b)3/2 (9)
Referring to FIGS. 10-12 next, .vertline..alpha..vertline., .vertline..beta..vertline., .vertline..gamma..vertline., .vertline..omega..sub.c .vertline., .omega..sub.c, .vertline..omega..sub.b .vertline., and .omega..sub.b in the case of 1-2 in FIG. 5 are respectively expressed in the following expressions (10)-(16). EQU .vertline..alpha..vertline.=(b-.DELTA.b)/2 (10) EQU .vertline..beta..vertline.=(b-.DELTA.b)/2 (11) EQU .vertline..gamma..vertline.=b+.DELTA.b (12) ##EQU3##
As shown in FIG. 11, D is in the counterclockwise direction with respect to C, following expressions are derived. EQU .omega..sub.c =.vertline..omega..sub.c .vertline. (14) ##EQU4## EQU .omega..sub.b =.vertline..omega..sub.b .vertline. (16)
With reference to FIG. 13, in the case of 2(b+.DELTA.b) in FIG. 5, error in the step C with respect to the step B is b+.DELTA.b. In this case, the alignment in the step D is desirably performed between the step B and the step C. Assuming the rotation error in the step D with respect to the step B is a, and the rotation error in the step D with respect to the step C is .beta., .alpha.and .beta.are expressed by the following expressions (17) and (18). EQU .alpha.=(-1) (b+.DELTA.b)/2 (17) EQU .beta.=(b+.DELTA.b)/2 (18)
Next with reference to FIGS. 14-16, .vertline..alpha..vertline., .vertline..beta..vertline., .vertline..gamma..vertline., .vertline..omega..sub.c .vertline., .omega..sub.c, .vertline..omega..sub.b .vertline., and .omega..sub.b in the case of 2-1 in FIG. 5 are respectively expressed by the following equations (19) to (25). EQU .vertline..alpha..vertline.=(b+.DELTA.b)/2 (19) EQU .vertline..beta..vertline.=(b+.DELTA.b)/2 (20) EQU .vertline..gamma..vertline.=b-.DELTA.b (21) ##EQU5##
As shown in FIG. 15, D is in the counterclockwise direction with respect to C, so that the following equations are derived. EQU .omega..sub.c =-(3b/2-1.DELTA.b/2) (23) ##EQU6## EQU .omega..sub.b =-(1b/2-3.DELTA.b/2) (25)
Referring to FIGS. 17-19, .vertline..alpha..vertline., .vertline..beta..vertline., .vertline..gamma..vertline., .vertline..omega..sub.c, .omega..sub.c, .vertline..omega..sub.b .vertline., and .omega..sub.b in the case of 2-2 in FIG. 5 are respectively expressed by the following equations (26) to (32). EQU .vertline..alpha..vertline.=(b+.DELTA.b)/2 (26) EQU .vertline..beta..vertline.=(b+.DELTA.b)/2 (27) EQU .vertline..gamma..vertline.=b+.DELTA.b (28) ##EQU7##
As shown in FIG. 18, since D is in the clockwise direction with respect to C, following equations are derived. EQU .omega..sub.c =.vertline..omega..sub.c .vertline. (30) ##EQU8## EQU .omega..sub.b =.vertline..omega..sub.b .vertline. (32)
Referring to above expressions (1) to (32), there are four patterns of the shot rotation error (.omega..sub.c, .omega..sub.b) in the case of 1-1, 1-2 in FIG. 5, according to the expressions (7), (9), (14) and (16), that is, -(b-.DELTA.b)/2, -(b-.DELTA.b)3/2, 3b/2+1.DELTA.b/2 and 1b/2+3.DELTA.b/2. There are also four patterns of the shot rotation error (.omega..sub.c, .omega..sub.b) in the case of 2-1, 2-2 in FIG. 5, according to the expressions (23), (25), (30) and (32), that is, -(3b/2-1.DELTA.b/2), -(1b/2-3.DELTA.b/2), (b+.DELTA.b)/2, and (b+.DELTA.b)3/2.
The maximum absolute value of the amounts of error in above eight expressions is (b+.DELTA.b)3/2 derived from the expression (32).
On the other hand, as for errors generated when the shot is not corrected by rotation, the maximum error in the step C with respect to the step B is .DELTA.b, and the maximum error in the step D with respect to the step B is .DELTA.b assuming that the constant error b is 0 in FIG. 5. As a result, the maximum error in the step D with respect to the step B becomes 2.multidot..DELTA.b. The value of the dispersive error (.DELTA.b) and the average value of the errors (b) are usually at the same level, and as a result of comparison between (b+.DELTA.b)3/2 and 2.multidot..DELTA.b, 2.multidot..DELTA.b is smaller than (b+.DELTA.b)3/2 by 3/2b-1/2.DELTA.b. This result indicates that the error is increased by 3/2b-1/2.DELTA.b in the case of the expression (32) in FIG. 19 compared with the case in which the shot is not corrected by rotation.
As described above, when the alignment in the step D is performed using data from separate steps regarding the X axis direction and the Y axis direction as shown in FIG. 3, the error is disadvantageously increased if the shot is corrected by rotation, compared with the case in which the shot is not corrected by rotation.